The salt potato sandwich is a Syracuse curiosity built on the premise that a starch can be a filling. The salt potato itself is a small, thin-skinned potato boiled in water so heavily salted it is nearly brine; the salt draws moisture out and leaves the flesh dense and creamy with a faint crust of dried salt on the skin. Put that between two slices of soft white bread, often with butter, and you have starch on starch, which is the whole improbable point. It is a regional in-joke that happens to taste like the inside of a very good potato, and the people who eat it know exactly how strange it is.
The craft is in the boil and the restraint. The salt ratio is the entire technique: enough salt that the water tastes like seawater, so the potatoes cook seasoned all the way through and emerge with a tight, almost waxy texture rather than a fluffy one. They are smashed lightly rather than mashed smooth, because the point is to keep some structure against the soft bread. Butter goes on warm so it melts into the potato and the crumb at once; the bread is plain white, deliberately, because anything with character would argue with a filling whose whole appeal is its plainness. Salt and pepper are usually the only additions, since the potato was already seasoned in the pot.
There is not much to vary here, and the sandwich is honest about that. Some builds add a slick of yellow mustard or a few rings of raw onion for a sharp note against the starch; a heartier reading folds in a slice of cheese or a strip of bacon and quietly turns it into a different sandwich. The salt potato itself belongs to the Syracuse summer table alongside corn and clambakes, and that context, like the other local starch-forward plates it sits beside, deserves its own article rather than being crowded in here.